Related papers: On non-uniqueness in the option valuation problem
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
Markov processes are well understood in the case when they take place in the whole Euclidean space. However, the situation becomes much more complicated if a Markov process is restricted to a domain with a boundary, and then a satisfactory…
In the junction $\Omega$ of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray $[\lambda_\dagger, +\infty)$ with a positive cut-off value $\lambda_\dagger$. We give two…
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this…
In this paper, we study the higher order Brezis-Nirenberg problem under the Navier boundary condition \be\label{eq} \begin{cases} (-\Delta)^m u=\varepsilon u+u^{p} & \text { in }\, \Omega, \\ u>0 & \text { in }\, \Omega, \\ u=-\Delta…
We consider exterior elliptic problems with coefficients stabilizing at infinity and study the critical value $\beta_{cr}$ of the coupling constant (the coefficient at the potential) that separates operators with a discrete spectrum and…
Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal…
In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional…
We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…
Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional…
The nonuniqueness of rational expectations is explained: in the stochastic, discrete-time, linear, constant-coefficients case, the associated free parameters are coefficients that determine the public's most immediate reactions to shocks.…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say,…
We investigate the issue of uniqueness of the limit flow for a relevant class of quasi-linear parabolic equations defined on the whole space. More precisely, we shall investigate conditions which guarantee that the global solutions decay at…
Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix…
We consider the nonlinear eigenvalue problem $ L u = \lambda f(u) $, posed in a smooth bounded domain $ \Omega \subseteq \Bbb{R}^{N} $ with Dirichlet boundary condition, where $ L $ is a uniformly elliptic second-order linear differential…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the…
In this paper, we extend and simplify the methods in [13] to improve the results on uniqueness of the boundary determination for the Maxwell equation. In particular, we show that the electromagnetic parameters are uniquely determined to…
In this note, we give a brief overview of obstacle problems for nonlocal operators, focusing on the applications to financial mathematics. The class of nonlocal operators that we consider can be viewed as infinitesimal generators of…